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Rectangular Arrangements

Problem

There are seven ways a 3x2 block can be placed inside a rectangle measuring 4x3.

How many ways can a 3x2 block be placed inside a rectangle measuring 8x6?


Solution

Consider the diagrams.

1st diagram: 7 times 4 = 28 positions for the block.
2nd diagram: 6 times 5 = 30 positions.

Giving 28 + 30 = 58 different positions for 3x2 block on an 8x6 rectangle.

How many positions can a 3x2 block be placed on an m x n rectangle?
What about different sized blocks?

Problem ID: 49 (Oct 2001)     Difficulty: 1 Star

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